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Ordinary Differential Equations and Applied Dynamics Commons™
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- Consistent event location (1)
- Detect-locate-restart (1)
- Discontinuous ODE (1)
- High-index differential-algebraic equations (1)
- Holonomic (1)
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- Inconsistent initial conditions (1)
- Monotone solutions (1)
- Multi-body systems (1)
- Non-holonomic (1)
- Nonautonomous ordinary differential equations (1)
- Post-stabilization (1)
- Runge-Kutta (1)
- Sedimenting sphere (1)
- Sim-ulation (1)
- Single-step methods (1)
- Sliding-mode control (1)
- Unilateral and bilateral discontinuities (1)
- Unsteady Stokes flow (1)
Articles 1 - 2 of 2
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman
Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman
All HMC Faculty Publications and Research
We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem
Simulation Of Engineering Systems Described By High-Index Dae And Discontinuous Ode Using Single Step Methods, Marc Compere
Simulation Of Engineering Systems Described By High-Index Dae And Discontinuous Ode Using Single Step Methods, Marc Compere
Publications
This dissertation presents numerical methods for solving two classes of or-dinary diferential equations (ODE) based on single-step integration meth-ods. The first class of equations addressed describes the mechanical dynamics of constrained multibody systems. These equations are ordinary differential equations (ODE) subject to algebraic constraints. Accordinly they are called differential-algebraic equations (DAE).
Specific contributions made in this area include an explicit transforma-tion between the Hessenberg index-3 form for constrained mechanical systems to a canonical state-space form used in the nonlinear control communities. A hybrid solution method was developed that incorporates both sliding-mode control (SMC) from the controls literature and post-stabilization from …